Direction of propagation for E field with amplitude in z direction

[yungman]

Please confirm the direction of propagation for me. If the E field is defined as:

$$\vec E \;=\; \frac{\mu_0 k}{2}(ct-|x|)\hat z$$

1) With this equation, the direction of propagation of the E field in both + and – x direction even though the $\vec E = \hat z E_z$?

2) The E field is not propagating along z axis at all even though $\vec E = \hat z E_z$. This only mean the amplitude of the E field is in z direction.
Can someone confirm this for me?

Thanks

Alan

 

[Doc Al]

I'd say you are correct.

 

[torquil]

Yes, the electric field vector points in the z-direction at all spacetime points (EDIT: except where/when it vanishes, of course...)

But how do you define "propagation"?

When plotted against x, the absolute value of the field strength looks like an upside-down V whose tip touches the x-axis at t=0. The pyramid rises linearly in time.

I guess you could use a Maxwell equation to find the B-field, and then form the Poynting vector which then tells you the energy flux.

 

[yungman]

Thanks guys for the quick reply. Yes, it is a inverse pyramid shape but I think the tip touching the z axis at t=0 instead and the base spread out in + and - x direction with time.